Differentiated Mathematicshttps://differentiatedmath.wordpress.com
Teaching math so everyone can learn.
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1 http://wordpress.com/https://s0.wp.com/i/buttonw-com.pngDifferentiated Mathematicshttps://differentiatedmath.wordpress.com
Project/Journal 11https://differentiatedmath.wordpress.com/2014/08/15/projectjournal-11/
https://differentiatedmath.wordpress.com/2014/08/15/projectjournal-11/#respondFri, 15 Aug 2014 20:12:22 +0000http://differentiatedmath.wordpress.com/?p=372Continue reading Project/Journal 11→]]>This was the year’s largest and most technical writing assignment. I required students to submit drafts which I edited and returned to them so they would have the chance to make their writing more precise. The project consumed a large chunk of our time, but the process of explaining their methods and results in writing, getting a draft edited, then trying to make their language more precise was a turning point for my students’ mathematical communication.

All but one of my students were seniors and were pretty well invested in learning about student loans. On Day One I introduced subsidized vs. unsubsidized student loans. (The project presents case studies using unsubsidized student loans.) I also addressed how student loan interest is actually calculated* and explained that A=Pe^(rt) would give good enough approximations. In the mish-mash curriculum I worked from, A=Pe^(rt) is used as an application for the natural log, so I wanted to give students experience using that formula even though the unit was not connected to other types of interest growth.

The project gives 3 cases:

You take out an unsubsidized student loan of $3000 your first semester of college and it grows while you attend school for 5 years.

You take out that same loan but you make an early payment of $500 two years into college.

You take out the same loan but a semester later.

*09/10/14: An improvement might be to ask students to give estimates or judgments on the three options before any calculation.

The first day’s assignment was to calculate what the debt would grow to by graduation in each case and estimate the cost of repayment. I left students pretty much to their own devices to figure it out, which frustrated them to no end.

On Day Two we compared their solutions, went over the correct solutions, and they worked on the first two paragraphs of the write-up, turning in drafts the next day. Then they worked on the edits and writing the next paragraph, turned in a new draft, etc. (See what I mean? Large chunk of our time.)

Although self-conscious about it, I decided to provide a scripted template for the write-up for two reasons: to get them to wrap their brains around formal technical writing before requiring them to produce it themselves, and to allow them to focus on the portions I cared about most without completely doing away with the rest. The first paragraph is almost entirely scripted, with just a couple blanks to fill in. The other paragraphs allow much more freedom. I’m sure the template could be improved, so don’t judge! However, feedback is welcome.

*Unfortunately, my initial understanding of how student loan interest accrues was faulty. I was able to get this explanation from the bank managing my husband’s student loan:

Student loans are considered simple interest loans. Interest accrues daily on the outstanding principal balance.
The calculation used to determine the amount of interest that accrues per day is as follows:

Total Unpaid Principal Balance x Interest Rate, Divided by 365 or 366 (Days in a Year)

]]>https://differentiatedmath.wordpress.com/2014/08/15/projectjournal-11/feed/0lesannoCh. 12 Student Loans Project ImageJournal 10: Reflect on Semester Onehttps://differentiatedmath.wordpress.com/2014/08/06/journal-10-reflect-on-semester-one/
https://differentiatedmath.wordpress.com/2014/08/06/journal-10-reflect-on-semester-one/#respondWed, 06 Aug 2014 15:57:11 +0000http://differentiatedmath.wordpress.com/?p=365Continue reading Journal 10: Reflect on Semester One→]]>Once again, we started a new semester with some reflection on what had gone before. This time I first asked them to choose five skills we’d worked on to rank in order of most understood to least understood. Then I asked them to write about the skills that were actually enjoyable to learn, and ended by having them reflect on their own actions and habits, good and bad.

]]>https://differentiatedmath.wordpress.com/2014/08/06/journal-10-reflect-on-semester-one/feed/0lesannoBeginning of Semester JournalJournal 9: Pre-final Venthttps://differentiatedmath.wordpress.com/2014/07/25/journal-9-pre-final-vent/
https://differentiatedmath.wordpress.com/2014/07/25/journal-9-pre-final-vent/#respondFri, 25 Jul 2014 23:23:39 +0000http://differentiatedmath.wordpress.com/?p=361Continue reading Journal 9: Pre-final Vent→]]>Journal 9 came right before the semester-one final, so I gave students a list of skills they’d been reviewing beside a continuum of fear adjectives and asked them to give vent to their states of mind. The value of the assignment lay in the combination of skill labeling, self-assessment, and end-of-semester therapy. There’s something to be said for letting students feel heard on a personal level in a math class.

Like several other journals I assigned this year, this one started as a fuzzy idea in my mind, then grew to have structure and support after I consulted with my assigned speech-language pathologist. Using the three sentence starters near the top, (N leaves me … because I …; One way I deal with this is …; I would rather N than…) the students first tried filling in blanks aloud in a class discussion. They seemed to enjoy that. Then I moved them to fleshing out their ideas in writing. I don’t think a single student wrote about the same topics they brought up in our discussion, which was interesting. Maybe they figured they’d already gotten those ones of their chests by the time they were writing.

*8/6/14. I listed all the skills as gerunds (solving…, remembering..., etc.), which fit perfectly into the “N leaves me …” sentence starter, but not into the “I would rather N than…” starter. The majority of my students failed to correct the grammar in the second case by changing solvingto solve, and so on. In the future, especially when working with students with language learning disabilities, I’ll want to draw the class’ attention to the necessary change.

]]>https://differentiatedmath.wordpress.com/2014/07/25/journal-9-pre-final-vent/feed/0lesannoCaptureProject 8: Function Arthttps://differentiatedmath.wordpress.com/2014/07/23/project-7-function-art/
https://differentiatedmath.wordpress.com/2014/07/23/project-7-function-art/#respondWed, 23 Jul 2014 19:18:27 +0000http://differentiatedmath.wordpress.com/2014/07/23/project-7-function-art/Continue reading Project 8: Function Art→]]>Instead of a journal, I assigned this Desmos art project to get kids working and experimenting with graphs. Next time I think I’ll make this first graphing project less free-form, asking them to make a specific image (a face?) or recreate a given pattern.

I improved the assignment sheet for a similar project given later in the year, but this is what I had managed to put together in time for Project 8.

]]>https://differentiatedmath.wordpress.com/2014/07/23/project-7-function-art/feed/0lesannoCh. 8 Desmos Graphing ProjectJournal 6: Rank the Solving Methodshttps://differentiatedmath.wordpress.com/2014/05/29/journal-6-rank-the-solving-methods/
https://differentiatedmath.wordpress.com/2014/05/29/journal-6-rank-the-solving-methods/#commentsThu, 29 May 2014 19:49:07 +0000http://differentiatedmath.wordpress.com/?p=343Continue reading Journal 6: Rank the Solving Methods→]]>Journal 6 asked students to rank the three quadratic solving methods they’d been working on: factoring, graphing, and the quadratic formula. This was the most heavily curriculum-related writing they’d had to do, which is probably why they struggled to describe the math with any specificity.

I liked having written evidence that preferences for solving methods differed, so I posted opposing excerpts in the classroom (for example, one student talked about preferring the factoring method, while another described how he hated that method the most).

]]>https://differentiatedmath.wordpress.com/2014/05/29/journal-6-rank-the-solving-methods/feed/1lesannoScreen shot 2014-05-29 at 3.37.02 PMJournal 5: Script of a Lessonhttps://differentiatedmath.wordpress.com/2014/05/29/journal-5-script-of-a-lesson/
https://differentiatedmath.wordpress.com/2014/05/29/journal-5-script-of-a-lesson/#respondThu, 29 May 2014 14:03:43 +0000http://differentiatedmath.wordpress.com/?p=338Continue reading Journal 5: Script of a Lesson→]]>Journal 5 was inspired by this fun post by Ben Orlin over at Math with Bad Drawings (it’s a script of trying to teach students that some ideas take time). I provided the text of his post for us to read/act out together, then asked students to come up with other lessons a math teacher might want her students to learn (I had to help the ideas along a bit). Finally, the assignment was for each student to pick one of those lessons and write a script of a teacher trying to teach that lesson to students.

The idea of a creative writing assignment in a math class is pretty cool already, but one that gets kids to consider the big-picture lessons they’re learning and engage in some teacher role playing sounds like a real winner. The kids were genuinely excited about this journal, and the scripts they turned in are some of the most enjoyable student writing I’ve ever graded. I made copies of them, and in my end-of-year nostalgia I’ve already flipped back to read them twice.

Some highlights:

A script that showed Niall Horan of One Direction learning that coming in to ask for help is not so bad after all.

A couple scripts that took all the personalities in our class and played up their characteristics.

A couple scripts that seemed like therapeutic coming-to-terms with past math class experiences.

Scripts that revealed different student approaches: some chose lessons they’ve already mastered and could make a good case for, while others chose those they need to work on.

*The optional math problem for students to include in their scripts was suggested by my co-conspiring SLP to provide students with some solid framework to hang their ideas on. Most students opted out of using it. For some it was essential.

]]>https://differentiatedmath.wordpress.com/2014/05/29/journal-5-script-of-a-lesson/feed/0lesannoScreen shot 2014-05-29 at 9.37.59 AMJournal 4: Mistakeshttps://differentiatedmath.wordpress.com/2014/05/28/journal-4-mistakes/
https://differentiatedmath.wordpress.com/2014/05/28/journal-4-mistakes/#respondWed, 28 May 2014 19:12:13 +0000http://differentiatedmath.wordpress.com/?p=332I’ve already talked here about this journal assignment , which I based on clips from Jo Baoler’s lesson about making mistakes, so I’ll just post the document. Here’s an editable version: Ch. 5 Post Test Mistakes Journal

]]>https://differentiatedmath.wordpress.com/2014/05/28/journal-4-mistakes/feed/0lesannoScreen shot 2014-05-28 at 3.04.59 PMJournal 3: Try Somethinghttps://differentiatedmath.wordpress.com/2014/05/28/journal-3-try-something/
https://differentiatedmath.wordpress.com/2014/05/28/journal-3-try-something/#respondWed, 28 May 2014 16:02:57 +0000http://differentiatedmath.wordpress.com/?p=327Continue reading Journal 3: Try Something→]]>Journal 2 should have been counted as a regular homework assignment, so I’ve jumped to Journal 3, where I started trying to change the anxious, mistake-fearing culture of the class. The text I excerpted from the Pacific Standard was difficult for students to digest, so we spent a good piece of time pulling the meaning out of the text. An editable version of the assignment can be downloaded here: Try Something Journal Prompt

]]>https://differentiatedmath.wordpress.com/2014/05/28/journal-3-try-something/feed/0lesannoScreen shot 2014-05-28 at 11.52.07 AMJournal 1: Reflect on Last Year’s Math Classhttps://differentiatedmath.wordpress.com/2014/05/27/journal-1-reflect-on-last-years-math-class/
https://differentiatedmath.wordpress.com/2014/05/27/journal-1-reflect-on-last-years-math-class/#respondTue, 27 May 2014 16:15:37 +0000http://differentiatedmath.wordpress.com/?p=322To get kids writing and self-assessing right off the bat, I gave this journal assignment on the first day of class. My collaborating SLP advised the inclusion of the word bank and sentence starters. Download an editable version here: 1 Day One Journal

Vocab Day: vocab review games, with emphasis placed on words from the current unit, although other words are included as well.

Study Guide, Day One: The study guide begins with a list of concepts, terms, or skills students will need for the upcoming test, then provides practice problems. To start things out we always read through the list of skills one by one, with a pause for self-assessment after each. The students discreetly show how confident they feel with each skill with a thumbs-up, thumbs-down, or thumbs-somewhere-in-between. They can use the rest of the period to work through practice problems.